Sains Malaysiana 51(11)(2022): 3807-3817

http://doi.org/10.17576/jsm-2022-5111-24

On the Impact of Asymmetric Dependence in the Actuarial Pricing of Joint Life Insurance Policies

(Kesan Kebersandaran Asimetri dalam Harga Aktuari Polisi Insurans Hayat Tercantum)

EMEL KIZILOK KARA^*

Department of Actuarial Sciences, Faculty of Arts and Sciences, Kirikkale University,

Kirikkale, Turkey

Received: 1 April 2022/Accepted: 19 July 2022

Abstract

Multipopulation mortality modeling is a significant research problem in actuarial science. Mortality functions involving multiple lives are also essential to determine the pricing of premiums. Moreover, the lifetime models based on dependence and asymmetry are more realistic. Hence, this paper applies an asymmetric copula model, Generalized FGM (GFGM) to model the bivariate joint distribution of future lifetimes. Premiums of first-death life insurance products are calculated based on the proposed model and compared with independent and symmetrical models. The results display that asymmetry has a significant effect on premium calculations. Also, it is concluded that the lowest premiums are generally in asymmetric lifetime models. This paper also provides analytical examples for the proposed model with Gompertz’s marginal law.

Keywords: Asymmetric dependence; copula; insurance; joint life (first-death); premium 

Abstrak

Pemodelan mortaliti populasi berbilang merupakan permasalahan penyelidikan yang penting dalam bidang sains aktuari. Fungsi mortaliti yang melibatkan model hayat berbilang juga berperanan untuk menentukan harga premium. Selain itu, model masa-hayat berdasarkan kebersandaran dan asimetri adalah lebih realistik. Oleh itu, makalah ini menggunakan model kopula asimetri dan Generalized FGM (GFGM) untuk memodelkan taburan tercantum bivariat bagi jangka hayat masa hadapan. Premium bagi produk insurans hayat kematian-pertama dihitung berdasarkan model yang dicadangkan dan dibandingkan dengan model tak bersandar dan simetri. Keputusan menunjukkan bahawa asimetri mempunyai kesan yang signifikan ke atas pengiraan premium. Selain itu, dapat disimpulkan bahawa premium terendah kebiasaannya ditunjukkan dalam model masa hayat asimetri. Kajian ini juga menyediakan contoh analisis bagi model yang dicadangkan menggunakan marginal Gompertz.

Kata kunci: Hayat tercantum (kematian-pertama); insurans; kebersandaran asimetri; kopula; premium

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^*Corresponding author; email: emel.kizilok@kku.edu.tr